Abstract
Modular flavor symmetry can be used to explain the quark and lepton flavor structures. The SUSY partners of quarks and leptons, which share the same superpotential with the quarks and leptons, will also be constrained by the modular flavor structure and show a different flavor(mixing) pattern at the GUT scale. So, in realistic modular flavor models with SUSY completion, constraints from the collider and DM constraints can also be used to constrain the possible values of the modulus parameter. In the first part of this work, we discuss the possibility that the S3 modular symmetry can be preserved by the fixed points of T2/ZN orbifold, especially from T2/Z2. To illustrate the additional constraints from collider etc on modular flavor symmetry models, we take the simplest UV SUSY-completion S3 modular invariance SU(5) GUT model as an example with generalized gravity mediation SUSY breaking mechanism. We find that such constraints can indeed be useful to rule out a large portion of the modulus parameters. Our numerical results show that the UV-completed model can account for both the SM (plus neutrino) flavor structure and the collider, DM constraints. Such discussions can also be applied straightforwardly to other modular flavor symmetry models, such as A4 or S4 models.
Highlights
Modular flavor symmetry can be used to explain the quark and lepton flavor structures
The SUSY partners of quarks and leptons, which share the same superpotential with the quarks and leptons, will be constrained by the modular flavor structure and show a different flavor(mixing) pattern at the GUT scale
In realistic modular flavor models with SUSY completion, constraints from the collider and DM constraints can be used to constrain the possible values of the modulus parameter
Summary
This minimal UV-completion S3 modular flavor SUSY GUT model has three additional SUSY breaking related free parameters c0, c1, F24/Λ in addition to the modulus parameter τ and other parameters chosen in the S3 modular SU(5) GUT model [13] to generate the flavor structure for quarks and leptons. It can be seen from the left-panel of figure 1 that the constraints from (I) to (III) can rule out much of the allowed parameter space of (τ ) versus (τ ), especially a large portion of the best-fit region of the SM(plus neutrino) flavor structure in [13]. It is interesting to note that the survived region of (τ ) versus (τ ) can still have a overlap with such best-fit region, which means that the UV-completed model can account for both the SM (plus neutrino) flavor structure and the collider, DM constraints. The survived region for the mass parameter F24/Λ, which is the only new mass parameter that determines the soft SUSY breaking scale at the GUT scale, is constrained to lie almost between 1.0 TeV to 4.8 TeV (see the upper-left panel of figure 2). No DM signal is anticipated to be found in the near-future DM direct detection experiments
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